Question: A certain factory produces and sells $x$ kilograms of ice cream per month. It costs $c$ dollars to produce one kilogram of ice cream, which is then sold for $0.16$ dollars. The factory's monthly net profit is $P$ dollars. Write an equation that relates $x$, $c$, and $P$.
Answer: The factory's net profit is equal to the factory's total income, reduced by the factory's total expenses. What is the factory's income from producing and selling $x$ kilograms of ice cream? What are the expenses? The income is $0.16x$ dollars: $\begin{aligned} &\phantom{=}\left(0.16\,\dfrac{\text{dollars}}{\text{kilogram}}\right)\left(x\,\text{kilograms}\right) \\\\ &=0.16\cdot x\,\dfrac{\text{dollars}}{\cancel\text{kilogram}}\cdot\,\cancel\text{kilograms} \\\\ &=0.16x\,\text{dollars} \end{aligned}$ Similarly, the expenses are $c\cdot x$ dollars. The net profit is then $0.16x$ minus $c\cdot x$ : $0.16x-c\cdot x=P$ This can also be written as $x(0.16-c)=P$.